Histograms

Histogram: Class width Range = Largest – Smallest

mpg of cars:

But…you can also just pick any scale as long as it is consistent.

mpg of cars:

Salaries of CEO’s (nearest thousand):

Using the calculator Put data in L1 Go to 2 nd y= Turn on, turn on histogram (make sure xlist is L1 or whatever list your data is in) Hit zoom9 Go to window. Set xmin to smallest value and scl = class width. Press graph. (Trace will show all values)

# credit card returns:

Cautions… Don’t confuse Histograms with Bar Graphs Don’t use count (in a frequency table) or percents (in a relative frequency table) as data. When comparing distributions with different numbers of observations you must use percentages instead of counts!

Central Tendency

Center Roughly describes where the center of the data is in the set. Can use the mean or the median

Mean Sample: Population:

The following show the # of hours spent by college professors in teaching and advising. Find the average # of hours they spend teaching & advising. Show your Work – including the formula that you used!

The 50 states plus the District of Columbia have a total of 3137 counties. There are a total of 248,709,873 people in each of these counties. Find the average population per county.

The following data represents the travel times to work of a sample of 15 North Carolina residents. Find the mean Key: 2|5 is a NC worker who travels 25 minutes to work. Do you think this represents the data well?

What if I used the Almanac Book of Facts and chose a few samples? Sample 1 20, ,978 15,384 13,931 24,960 Sample 2 28,895 10,032 16, ,275 30,797 Sample 3 16, ,478 14, ,859

We’ll study this further to see how to be able to use samples to predict the populations better.

Median This is the value in the middle 50% of the data is above and below this value.

Find the Median – first put the values in order (smallest to largest) 6, 8, 12, 14, 17 7, 15, 22, 23, 27, 28 Median = 12

The following data represents the travel times to work of a sample of 15 North Carolina residents. Find the median Key: 2|5 is a NC worker who travels 25 minutes to work. Do you think this represents the data well?

The mean is greatly affected by outliers – it’s very sensitive to them – which means it is pulled towards the outlier. The median is insensitive to outliers. It’s often used more because it is more stable.

Examples Average salaries of professional football players. Scores on a test when there’s one that hasn’t been made up yet. Average salaries of 1 st year teachers

Ed took 5 tests and his average was 85. If his average after the first three tests was 83, what’s the average of the last two tests.

On Thursday, 20 out of 25 students took a test and their average was 80. On Friday, the other 5 students took it and their average was 90. What was the class average?

The first 3 hours of a trip, Susan drove 50 mph. Due to delays, she drove 40 mph for the next 2 hours. What was her average speed?

Ed’s average on 4 tests is 80. What does he need to get on the 5 th test to raise his average to an 84?

Homework Page 45 (53, 55, 56, 59, 65, 79, 81, 83, 85)